Poythress V.S. Logic: A God-Centered Approach to the Foundation of Western Thought

Crossway, 2013. — 736 p. — ISBN 978-1-4335-3229-0, 978-1-4335-3230-6, 978-1-4335-3231-3, 978-1-4335-3232-0.For Christians looking to improve critical thinking skills, here is an accessible introduction to the study of logic as well as an in-depth treatment of the discipline from a professor with six academic degrees and over 30 years experience teaching. Questions for further reflection are included at the end of each chapter as well as helpful diagrams and charts for use in college and graduate-level classrooms.
Vern Poythress has undertaken a radical recasting of the study of logic in this revolutionary work from a Christian worldview.Tables and Illustrations
Symbols Used in Parts II–IV
PrefaceElementary Logic
Introducing Logic and Argument
Logic in Tension
Why Study Logic?
What Do We Trust?
Formal Logic
Inductive Logic
The Importance of Formal Logic
God in Logic
Logic Revealing God
Logic as Personal
Logic within Language
Suppressing the Truth
Logic and the Trinity
The Absoluteness of God
Logic and Necessity
Transcendence and Immanence
Reflections on the Mediation of Human Knowledge of Logic
Fallacies and God
The Problem of Classification
Analogy
Unity and Diversity
Stability of Meaning
Form and Meaning
Context for Meaning
Persons and Logic
Logic and Religious Antithesis
Theistic Proofs
Rethinking Western Thought
Aristotelian Syllogisms
Theistic Foundations for a Syllogism
Venn Diagrams
Syllogisms of the First Figure
Checking Validity by Venn Diagrams
Aspects of Propositional Logic
Truth in Logic
Truth in Logic: Truth Functions
Divine Origin of Logical Functions
Complex Expressions
Perspectives on Truth in Logic
Venn Diagrams for Truth Functions
Other Representations of Logical Truth and Falsehood
Boolean Algebra
Truth-functional Equivalence
Harmony in Truth
Perspectives on Truth Functions
Propositional Logic
Introducing Propositional Logic
Axioms of Propositional Logic
Alternative Axioms
Dispensing with Axioms
Perspectives on Propositional Logic
Soundness and Completeness of Propositional Logic
Imitations of TranscendenceEnriching Logic
Predicate Logic
Introducing Predicate Logic
Theistic Foundations for Predicates
Quantification
The Theistic Foundation for Quantification
Axioms and Deductions for Quantification
Soundness of Quantification
Including Equality and Functions
Equality
Functions
Introducing Formal Systems
Troubles in Mathematics
Axiomatizing Mathematics
Studying Proofs
Theistic Foundations for Proof Theory
A Computational Perspective
Theistic Foundations of Computation
Models
Theistic Foundations for Models
Special Logics and More Enriched Logics
Higher-order Quantification
Multivalued Logic
Intuitionistic Logic
Modal Logic
Theistic Foundations for Modal Logic
Models for Modal Logic
ConclusionSupplements
Supplements to Elementary Logic
Antinomies with Sets: The Set of All Sets and Russell’s Paradox
Deriving Syllogisms of the First Figure
Syllogisms of the Second Figure
Syllogisms of the Third and Fourth Figures
Supplementary Proofs for Propositional Logic
Some Proofs for Boolean Algebra
Deriving Whitehead and Russell’s Axioms
Practice in Proofs
The Rule of Replacement
Reasoning toward the Completeness of Propositional Logic
Proofs for Quantification
Deductions of Rules for Quantification
Natural Deduction of Syllogisms
Proofs for Formal Systems
Introducing Gödel’s First Incompleteness Theorem
Simple Proofs within a Formal System
Deriving Natural Deduction and the Associative Axiom
Helping Lemmas
Other Proofs
The Halting Problem for Computer Programs
Diagonalization
Philosophy and Logic
Kantian Subjectivism
The Role of Logic in Philosophy
A View of Modern Logic
Modal Ontological Argument
Reforming Ontology and LogicBibliography
General Index
Scripture IndexTrue PDF